2v^2=13v+2

Solution for 2v^2=13v+2 equation:

Simplifying
2v2 = 13v + 2

Reorder the terms:
2v2 = 2 + 13v

Solving
2v2 = 2 + 13v

Solving for variable 'v'.

Reorder the terms:
-2 + -13v + 2v2 = 2 + 13v + -2 + -13v

Reorder the terms:
-2 + -13v + 2v2 = 2 + -2 + 13v + -13v

Combine like terms: 2 + -2 = 0
-2 + -13v + 2v2 = 0 + 13v + -13v
-2 + -13v + 2v2 = 13v + -13v

Combine like terms: 13v + -13v = 0
-2 + -13v + 2v2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-1 + -6.5v + v2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -6.5v + 1 + v2 = 0 + 1

Reorder the terms:
-1 + 1 + -6.5v + v2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6.5v + v2 = 0 + 1
-6.5v + v2 = 0 + 1

Combine like terms: 0 + 1 = 1
-6.5v + v2 = 1

The v term is -6.5v.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5v + 10.5625 + v2 = 1 + 10.5625

Reorder the terms:
10.5625 + -6.5v + v2 = 1 + 10.5625

Combine like terms: 1 + 10.5625 = 11.5625
10.5625 + -6.5v + v2 = 11.5625

Factor a perfect square on the left side:
(v + -3.25)(v + -3.25) = 11.5625

Calculate the square root of the right side: 3.400367627

Break this problem into two subproblems by setting 
(v + -3.25) equal to 3.400367627 and -3.400367627.

Subproblem 1
v + -3.25 = 3.400367627

Simplifying
v + -3.25 = 3.400367627

Reorder the terms:
-3.25 + v = 3.400367627

Solving
-3.25 + v = 3.400367627

Solving for variable 'v'.

Move all terms containing v to the left, all other terms to the right.

Add '3.25' to each side of the equation.
-3.25 + 3.25 + v = 3.400367627 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + v = 3.400367627 + 3.25
v = 3.400367627 + 3.25

Combine like terms: 3.400367627 + 3.25 = 6.650367627
v = 6.650367627

Simplifying
v = 6.650367627

Subproblem 2
v + -3.25 = -3.400367627

Simplifying
v + -3.25 = -3.400367627

Reorder the terms:
-3.25 + v = -3.400367627

Solving
-3.25 + v = -3.400367627

Solving for variable 'v'.

Move all terms containing v to the left, all other terms to the right.

Add '3.25' to each side of the equation.
-3.25 + 3.25 + v = -3.400367627 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + v = -3.400367627 + 3.25
v = -3.400367627 + 3.25

Combine like terms: -3.400367627 + 3.25 = -0.150367627
v = -0.150367627

Simplifying
v = -0.150367627

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {6.650367627, -0.150367627}